Results 211 to 220 of about 6,335 (253)

Non-commutative Henselian rings

Journal of Algebra, 2009
Non-commutative Henselian rings are defined and some basic properties of them are discussed. It is shown that a local ring which is complete in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.
Aryapoor, Masood,, Aryapoor, Masood, Masood Aryapoor   +2 more
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ON THE COMMUTING GRAPH OF RINGS

Journal of Algebra and Its Applications, 2011
Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R\Z(R) and two vertices a and b are adjacent if ab = ba. It has been shown that the diameter of Γ(R)c is less than 3. For a finite ring R we show that the diameter of Γ(R)c is one if and only if R is the non-commutative ring on 4 elements.
Omidi, G. R., Vatandoost, E.
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Almost-Commutativity in Rings

Acta Mathematica Hungarica, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bell, H. E., Klein, A. A.
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COMMUTATIVE TALL RINGS

Journal of Algebra and Its Applications, 2014
A ring is right tall if every non-noetherian right module contains a proper non-noetherian submodule. We prove a ring-theoretical criterion of tall commutative rings. Besides other examples which illustrate limits of proven necessary and sufficient conditions, we construct an example of a tall commutative ring that is non-max.
Penk, Tomáš, Žemlička, Jan
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Commutativity of Rings with Constraints on Commutators, II

Results in Mathematics, 2000
[For part I see ibid. 5, 123-131 (1985; Zbl 0606.16023).] The author proves commutativity of an associative ring \(R\) satisfying one of the following conditions: (1) for each \(x,y\in R\) there exists a co-monic polynomial \(p(t)\in tZ[t]\), such that \([x,y]=[x,y](p(xy)-p(yx))\); (2) for each \(x,y\in R\) there exist \(p(t),q(t)\in tZ[t]\) with \(q(t)
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A commutativity property for rings

Journal of Algebra and Its Applications, 2015
We provide a partial answer to the following question: Assume that R is a finite ring of order s such that for every two subsets M and N of cardinalities m and n respectively, there exist x ∈ M and y ∈ N such that xy = yx. What relations among s, m, n guarantee that R is commutative?
Bell, H. E., Zarrin, M.
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Metaideals in Commutative Rings

Algebra Colloquium, 2005
New examples of metaideals in commutative rings are constructed. It is proved that metaideals of a commutative ring form a sublattice of the lattice of all subrings, and for any subring A of a commutative ring P, there exists the largest subring Mid P (A) (called metaidealizer) in which A is a metaideal. Metaidealizers in several cases are described.
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On Commutative Splitting Rings

Proceedings of the London Mathematical Society, 1970
Abstract not ...
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Commutativity of rings with powers commuting on subsets

Mathematical Journal of Okayama University, 1997
Let \(R\) denote a ring with 1; let \(w=w(X,Y)\) denote a word, possibly 1, in two noncommuting indeterminates; and let \(n\) be a positive integer. The elements \(x,y\in R\) are said to satisfy condition \(a(w,n)\) (resp. \(b(w,n)\)) if \(w(x,y)[x^n,y^n]=0\) (resp. \(w(x,y)((xy)^n-(yx)^n)=0\)). Define \(A\subseteq R\) to be a \(P\)-subset if for each \
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IDEALS IN COMMUTATIVE RINGS

Mathematics of the USSR-Sbornik, 1976
This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes ...
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